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Workshop: NeurIPS 2023 Workshop: Machine Learning and the Physical Sciences

The search for the lost attractor

Mario Pasquato · Syphax Haddad · Pierfrancesco Di Cintio · Alexandre Adam · Noé Dia · Mircea Petrache · Ugo Niccolò Di Carlo · Alessandro Alberto Trani · Laurence Perreault-Levasseur · Yashar Hezaveh · Pablo Lemos

Abstract: N-body systems characterized by $r^{-2}$ attractive forces may display a self similar collapse known as the gravo-thermal catastrophe. In star clusters, collapse is halted by binary stars, and a large fraction of Milky Way clusters may have already reached this phase.It has been speculated -with guidance from simulations- that macroscopic variables such as central density and velocity dispersion are governed post-collapse by an effective, low-dimensional system of ODEs. It is still hard to distinguish chaotic, low dimensional motion, from high dimensional stochastic noise. Here we apply three machine learning tools to state-of-the-art dynamical simulations to constrain the post collapse dynamics: topological data analysis (TDA) on a lag embedding of the relevant time series, Sparse Identification of Nonlinear Dynamics (SINDY), and Tests of Accuracy with Random Points (TARP).

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